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it's easier to look at the route on strava. it has it's own problems in that getting into the correct lane outside south wimbledon to go straight on is impossible if you use the segregated cycle lane and dorset road in spite of being 20mph and covered in speed bumps attracts speeders as it's a common rat run and they love to crowd you and overtake at the narrowest points but it's better than the main road.
I think we share a commuting route. I'd be interested to hear what your detour is. I cut through the park in the summer to avoid that bridge, but it's rather Somme-like on wet days, so not really an option for much of the winter.